Randolph Taylor, a 38-year-old Vietnam War veteran depressed about his failure to keep a job as a police officer and his encounters with the Veterans Administration, left California last month to seek treatment at a VA hospital here.

In the predawn hours yesterday, police said, Taylor stood at the Vietnam Veterans Memorial, aimed a .38 caliber gun and shot himself in the right side of the chest. Last night he was listed in fair condition at George Washington University Hospital.

Taylor became the second Vietnam Veteran to shoot himself near the memorial in the past four months. On Sept. 18, Jeffrey Charles Davis, a 36-year-old Vietnam veteran and a D.C. police officer, fatally shot himself while facing the stark, black wall at 21st Street and Constitution Avenue NW.

Park Police Maj. Richard Cusick said Taylor was standing at the base of the statue of three servicemen that faces the memorial's black granite wall when he shot himself shortly before 3 a.m. Cusick said Taylor earlier talked with members of a group of veterans who stand vigil at the memorial 24 hours a day.

"One of these individuals said he went up to the foot of the statue, saw Taylor was holding a gun, and called police," said Cusick. "The officers arrived at the scene but had no vocal contact with the man before he pulled the trigger."

"Randy is a Vietnam veteran, with a lot of medals," said a friend he called Monday, Judy Forsberg. "He has been ignored and treated as unimportant by the establishment. What is a person supposed to do? I don't think anyone else would persevere as much as he has," said Forsberg, who said she is the director of a California women's organization.

Taylor, in a telephone interview from his hospital room, said, "The San Francisco Police Department took away my job and the VA took my pension. What am I going to do? I have nobody, but somebody has to do something."

People who know Taylor say he has often been under severe stress since returning from Vietnam. But his problems grew after he applied to join the San Francisco Police Department in 1980.

Bill Wallace, a reporter for the San Francisco Chronicle who wrote stories on Taylor, said, "The Civil Service Commission voted 3 to 1 against allowing him to join in March 1980. They didn't want to let him in because he had been depressed. Randy filed a suit in 1981 and got a court order that said the commission was bound by a city- appointed psychiatrist, who said he had overcome his emotional problems."

When Taylor joined the department his veteran's pension was stopped, said Sgt. Jesse Brown of the San Francisco Police Department's personnel division. Brown said that, according to police records, Taylor was a police officer from Jan. 4 to Nov. 30, 1982.

"He was terminated during his probationary period for failing to meet department standards in the field training program," said Brown. "He had passed the police academy training."

"His pension was supposed to be restored after he lost his job," said Forsberg, "but it was mired in red tape."

"He had a service-related disability due to stress," Brown said. "He had some stress and alcohol problems, but I guess he overcame them." According to Wallace, Taylor served in the Marine Corps for 42 months and was wounded three times in Vietnam. Marine Corps officials said yesterday they needed to check their records before they could provide any information.

According to San Francisco police records read by Brown, Taylor said he earned a B.S. in Mass Communications from Virginia Commonwealth University and studied criminology at San Francisco City College. He listed an address in Richmond as the place where he lived previously and named a brother and sister in San Francisco as next of kin.

In San Francisco, Taylor attempted to call public attention to the plight of Vietnam veterans through a 40-day fast that started last May. He ended the fast July 4, after the Democratic National Committee agreed to allow someone to address the national convention on the issue of veterans' rights.

"Randy was disappointed that no one ever asked him to address the convention," said Forsberg. "He's not even sure it was done. He felt betrayed."

Yesterday, veterans who gathered at the memorial talked about the morbid allure of the smooth black granite wall that lists the names of those killed in the war.

"There are lots of reasons for veterans to go there," said Dr. Bennett Jennings, a clinical psychologist at the Veteran's Center in Southeast. "They go there in a sense to be with friends. They feel that when they die they'll be with these friends."

"If my husband has something on his mind to sort out . . . he'll go to the wall . . . " said Kathleen Renault. "He doesn't care if it's 2 a.m., raining and below zero. All the guys are like that. There's something about the wall. It's like a magnet."